You are given a magical spring which has an odd restoring force, F = -kx², THIS IS NOT THE TYPICAL SPRING RESTORING FORCE (remember, this is a magical, supernatural spring!) calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? c) If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity of the mass?

You are given a magical spring which has an odd restoring force, F = -kx², THIS IS NOT THE TYPICAL SPRING RESTORING FORCE (remember, this is a magical, supernatural spring!) calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? c) If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity of the mass?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A particle of mass moves in 1 dimensional space with the following potential energy: (in figure)…

A: The potential energy of a particle moving in 1-D is given by the function, U(x)=Uo[2(xa)2-(xa)4]…

Q: An object of mass m r = ro 1+cos 0 moves in a parabolic trajectory given by (ro = 12). mk a)…

Q: A particle of mass m moves along the x-axis such that its acceleration is d²x dz² = 8x³. -X. (a)…

Q: An object is traveling along the y axis with the potential energy shown in the figure. If the object…

Q: Show that the combined spring energy and gravitational energy for a mass m hanging from light spring…

A: Step 1The reference level for gravitational potential energy is set midway between the unstretched…

Q: If this piece of abductin is 3.8 mm thick and has a cross-sectional area of 0.60 cm², how much…

A: Given A scallop forces open its shell with an elastic material called abductin, whose Young's…

Q: Consider a spring (k=12.50 N/m) attached to a wall, compressed a distance 0.58 m by a 0.24 kg mass…

Q: SF-2 The force required to stretch (elongate) a spring is shown in the graph to the right. a) Find…

A: Given:- The force required to stretch a spring is shown in the graph as Find:- a) The spring…

Q: The 45-lb block rests on the rough surface for which the coefficient of kinetic friction is = 0.2.…

Q: When a spring is stretched by 1.00 m, its spring potential energy is 20 J. What is the spring…

A: The stretching in spring is The spring potential energy is Note:Find:(a) Spring constant.(b)…

Q: A 7 kg box moving at 6.52 m/s on a horizontal, frictionless surface runs into a light spring of…

A: Given data: Mass (m) = 7 kg Horizontal speed (v) = 6.52 m/s Spring constant (k) = 67 N/m Required:…

Q: Consider a mass and spring system. If the mass is pulled by distance x, stretching the spring by x,…

A: We have given a mass-spring system. The mass is pulled by distance x.

Q: As shown in the figure below, two masses m, = 4.30 kg and m, which has a mass 50.0% that of m,, are…

Q: Suppose a certain spring’s relaxed length is 13 cm. (a) If we must put 50 J of energy into the…

A: The potential energy stored in a spring is given by:Where: is the potential energy stored in the…

Q: I performed a lab using a toy car to go down a ramp that was positioned at different heights. For…

A: Given data: The mass of the car is m=0.56 kg The height of the ramp is d=0.4 m Write the…

Q: answer the following question "When is the velocity of the mass at a maximum? Justify your answer"…

Q: What is the ratio of the Force required to hold a spring at 4m past its natural length to the Force…

A: Force on a spring is given as where k is the spring constant, x is the spring stretch or…

Q: When a 4 kg object is hung vertically on a certain light spring that obeys Hooke's Law, the spring…

A: Given:- vertically hung object mass = 4 kg spring stretches =2.50 cm Find:- work must…

Q: (a) A spring exerts a force of 7.2N when stretched 1.2m beyond its natural length. Assuming that…

A: (a) Given value--- Force = 7.2 N. x = 1.2 m. We have to find--- work done? (b) Given value---…

Q: In terms of X, how much is compressed to store twice as much potential energy and half as much…

A: Elastic potential energy,

Q: Work of 1 Joule done in stretching a spring from its natural length to 16 cm beyond its natural…

A: The work needed to stretch a spring is equal to the elastic potential energy stored in the spring…

Q: An object hangs motionless from a spring. When the object is pulled down and held, what happens to…

Q: (d) If the particle is very close to the origin (x approximated as that of a simple harmonic…

Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

100%

You are given a magical spring which has an odd restoring force, F = -kx², THIS IS NOT THE TYPICAL SPRING
RESTORING FORCE (remember, this is a magical, supernatural spring!) calculate:
a) The work done by an external force stretching the spring a distance L away from the equilibrium length.
b) At a stretch length L, how much potential energy is stored in the spring?
c) If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity
of the mass?
d) At what x coordinate does this maximum velocity occur?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop). c)What is the child's final speed, vf in m/s?
An ideal Spring of negligible mass is 12,00 cm long when nothỉng is attached to ît, When you hang a 3,15-kg weight from it, you measure ſts length to be 13.40 cm, If you wanted to store 10,0 J of potential energy in this spring, what would be ſts total length?
If you are running with speed of 6 m/s and your weight is 800 N. Find out (a)your mass, (b) your kinetic energy, (c) If you live on 2nd floor that is 5 m above the ground, then how much potential energy you will have.
SQU is trying a new particle accelerator design with a mechanical component using a spring that does not obey Hooke's law. When stretched/compressed x metres, it exerts a force of 39.6x+51.6x2 (a) Compute the work required to stretch the spring from x= 1.0 m to x 1.3 m.
A certain spring is found not to obey Hooke's law; it exerts a restoring force F(x) = -ax² - 6x³ if it is stretched or compressed, where: a = 10.0N/m², B = 300.0N/m³ The mass of the spring is negligible. Calculate the potential energy function U(x) for this spring, if U(x=0) = 0. Find the spring potential energy at x = 0.500 m
E21) a)Write the work done by a conservative force in terms of its potential energy. b)In what direction are forces pointing to be considered centripetal? c)In a system of interacting particles, what conservation law results when ∑Fiext=? d)Anobjectexperiencingseveralforcesresultinginsomedisplacement.What is the net work done by these forces equal to If the work of one of these forces is path-dependent, then what is not conserved? e) If a frictional force causes the total mechanical energy of a system to decrease, then I) what happens to the system’s total internal energy? ii) what is truly conserved?